• Use to solve any LPs with the variables n > 2

• Define each constraint a slack variable to convert it to equalities

• Define each constraint an excess  or surplus variable to convert it to equality.

• Transform the LP to its standard form.

• Present the standard form in Simplex Table.

• Check for the most negative number from the non-basic variables.

• Find any positive number so that it satisfies the criterion : min{ (value column 1/x_1),(value column 2/x_2)}.

• Take the denominator of the division above that gives the  least value as our pivot element.

• Change the pivot row by dividing each number by the pivot element.

• All the numbers in the pivot column must be set to zeroes except the pivot element which is replaced by 1.

• The remaining numbers in the non-pivot rows are calculated using ' rectangular rule'.

Two different ways the simplex method can be used.

1) Method 1
Multiply the objective function for the min problem by -1.
Solve the problem as a max problem with the objective function -z.
(optimal z-value for min)= -(optimal z-value for max).
2)  Method 2
Choose the variable with the most positive coefficient in last row as pivot column if any nonbasic variable has a positive coefficient.
Find the pivot element using ratio test.

This method is used to solve LP problem with > or = constraints.

In choosing variable, use the more positive or more negative.

1) In max problem
All artificial variables will be zero by adding a term -Ma.
2) In min problem
Add a term Ma to objective function.